The present paper studies the effects of bandwagon and underdog on the political equilibrium of two-party competition models. We adapt the generalized Wittman-Roemer model of political competition for voter conformism, which views political competition as the one between parties with factions of the opportunists and the militants that Nash-bargain one another, and consider three special cases of the general model: the Hotelling-Downs model, the classical Wittman-Roemer model, and what we call the ideological-party model. In the Hotelling-Downs model, where the militants have no bargaining power in both parties, political parties put forth an identical policy at the equilibrium, regardless of the type of voter conformism, and this is the only equilibrium. Thus neither bandwagon nor underdog has any effect on the Hotelling-Downs political equilibrium. In both the ideological-party and classical Wittman-Roemer models, parties propose differentiated policies at the equilibrium, and the extent of policy differentiation depends on the degree of voter conformism. In these models, multiple equilibria generically exist when the bandwagon effect is sufficiently strong. We characterize the relationship between the extent of voter conformism and equilibrium party platforms in dynamically stable equilibria of these models.